Two more

Square roots

Generated by a program similar to the last two pictures on Monday's post, but the functions are +\sqrt{z}, -\sqrt{z} and 1+z. Don't plot a point if the last operation was 1+z, and colour points according to the operation used 5 iterations ago.

Golden ratio

Similar to the third image on Monday's post, but when we multiply by \i we also multiply by the golden ratio \displaystyle \frac{1}{2}(1+\sqrt{5}) = 1.618... Most the rectangles you see in this image are golden rectangles, which are supposedly the most aesthetically pleasing.

This entry was posted on Wednesday, September 3rd, 2008 at 4:00 pm and is filed under fractals. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

2 Responses to “Two more”

  1. Kaz Maslanka says:
    September 3, 2008 at 11:38 pm

    It certain that the golden rectangle is sublime in its beauty by way of the aesthetics of mathematics however, it is no more beautiful than a box of corn flakes by the aesthetic criteria of art.

    Bottom line is that your image is wonderful! it is just have very little to do with art.

    Reply
  2. admin says:
    September 4, 2008 at 8:37 pm

    Actually, it is artists, not mathematicians, who have claimed that the golden rectangle is the one with the most pleasing aspect ratio. It has been incorporated into a great deal of art from ancient Greek architecture to the drawings and paintings of Leonardo da Vinci. While there are some neat mathematical qualities to this number, I don't think there are any mathematical reasons for it to be considered the most aesthetic - it seems to be more a piece of artistic lore.

    Reply

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